Beilinson–Parshin Adeles via Solid Algebraic Geometry
Abstract
Abstract We apply Clausen–Scholze’s theory of solid modules to the existence of adelic decompositions for schemes of finite type over $\mathbb{Z}$. Specifically, we use the six-functor formalism for solid modules to define the skeletal filtration of a scheme, and then we show that decomposing a quasi-coherent sheaf with respect to this filtration gives rise to a new construction of the Beilinson–Parshin adelic resolution. As an application of the adelic decomposition combined with some nice completeness properties of the solid tensor product, we prove a version of adelic descent for solid quasi-coherent sheaves.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Polynomial and algebraic computation
Commutative Algebra and Its Applications
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 8
- Publication date
- 26 March 2026
- Language
- EN